SMA vs EMA: Simple vs Exponential Moving Average Explained

A simple moving average (SMA) gives every close in its window the same weight; an exponential moving average (EMA) gives the most recent close the most weight and older closes steadily less. That makes the EMA react faster to a new price, while the SMA moves more evenly and changes only as closes enter and leave its window. Vyreon reports SMA 20, 50, 100 and 200 and EMA 12 and 26.

SMA Formula

SMA(n) = (sum of the last n closes) ÷ n

Each close in the window counts for 1/n. For a 20-day SMA that is 5% each; for a 200-day SMA, 0.5% each. A close older than n sessions counts for nothing.

EMA Formula

EMA today = EMA yesterday + α × (close − EMA yesterday), with α = 2 ÷ (n + 1)

The newest close gets weight α, the one before α × (1 − α), and so on, shrinking each session without ever reaching zero. For a 20-day EMA, α = 2/21 ≈ 9.5%, almost double the SMA's 5%. For a 12-day EMA, α ≈ 15.4%.

An EMA needs a starting value. Vyreon starts each EMA from the simple average of its first n closes, then applies the formula. Tools that start from a different date can show slightly different EMA values.

SMA Vs EMA Lag

Both averages lag the price because they include older closes. With α = 2/(n + 1), the EMA's average age of data is the same as the SMA's: (n − 1)/2 sessions, or 9.5 sessions for n = 20. The difference is how that lag plays out.

First reaction: the EMA moves more on the day of a new close, because the newest close carries more weight.
Full adjustment: the SMA fully reflects a new price level after n sessions; the EMA approaches it gradually and never fully gets there.
Drop-off effect: the SMA can move when an old close leaves the window, even if today's price is unchanged. The EMA has no window edge, so it has no drop-off effect.

Illustrative example: a price sits at 100 for months, then moves to 110 and stays there. After 1 session the 20-day SMA is 100.50 and the 20-day EMA about 100.95. After 10 sessions the SMA has covered 50% of the move (105.00) and the EMA about 63% (106.32). After 20 sessions the SMA is at 110.00, while the EMA has covered about 86% (108.65).

Which Moving Average Reacts Faster?

The EMA reacts faster to the latest closes; the SMA catches up completely sooner after a step change. Neither is more accurate. They summarize the same closes with different weights, and shorter windows of either kind follow the price more closely than longer ones.

How Vyreon Uses Each

SMA 20, 50, 100 and 200: reference lines for roughly one, two and a half, five and ten months of sessions. The 50- and 200-day SMAs feed the distance-from-average figures, the 50/200 state, golden and death crosses, and the side of the 200-day with its session count.
EMA 12 and 26: the building blocks of MACD, and reported in their own right.
EMA 20: the middle line of the Keltner channel (see price channels).

All are computed on daily closes adjusted for splits and dividends, so a split does not appear as a crash through the average.

What The SMA And EMA Do Not Tell You

Both describe past closes and always lag. Neither predicts the next move.
Crossovers between averages, or between price and an average, are conventions, not forecasts.
The window length and weighting are choices; different settings draw different lines from the same prices.

Sources

John J. Murphy, Technical Analysis of the Financial Markets (New York Institute of Finance, 1999): simple and exponential moving averages.
Robert G. Brown, Statistical Forecasting for Inventory Control (1959): exponential smoothing.
Gerald Appel, who developed MACD in the late 1970s; Technical Analysis: Power Tools for Active Investors (FT Press, 2005): the 12- and 26-day EMAs in MACD.